Chapter 9 GARCH Models with CPPI Application

Purpose – The aim of this chapter is to examine the constant proportion portfolio insurance (CPPI) method when the multiple is allowed to vary over. Methodology/approach – A quantile approach is introduced under the dependent return hypothesis. We use for example ARCH-type models. Findings – In this framework, we provide explicit values of the multiple as function of the past asset returns and other state variables. We show how the multiple can be chosen to satisfy the guarantee condition, at a given level of probability and for particular market conditions. Originality/value of paper – We show in this chapter that it is possible to choose variable multiples for the CPPI method if quantile hedging is used and in the case of dependent log returns. Upper bounds can be calculated for each level of probability and according to state variables. This new multiple can be determined according to the distributions of the risky asset log return and volatility.